I cannot figure out how to Rig Eyes
First off you're going to want the pupil and white connected on the same surface. having them disconnected can only lead to strange shadows and collisions like this. The best way to set up eyes so that there are no strange collisions like this is to make a sphere for the eyes. once you have the sphere you place the 3D cursor in the center of it (key stroke : shift+S > U aka cursor to selection) then select your eye bone and put the Head in the cursor at the center of the eyes (Shift+S > T) and then put the tail in the center of the pupil. Now the eye will rotate from the center of the sphere and therefore the pupil will stay flush against the surface of the sphere no matter what direction you rotate it.